Saturday, November 14, 2009

Optimal Exits

Synopsis:An optimal exit strategy of non-catastrophic (ie not discontinuous) nature can always be found .

Discussion .

The proof is found by simply reversing Catastrophe Theory , which has well-proven theoretical mathematical underpinnings . The actual catastrophe acts as a trapdoor-function , but it has lead-ins .

Care has to be taken with perfect hindsight . It becomes two questions :1.Can an exit strategy always be found with perfect hindsight ? The answer is yes , except if a naked singularity is involved . Then cases can exist where there are no conceivable warnings , no matter how perfect the information .

2. Can an exit strategy be found with imperfect present knowledge ?This amounts to identifying the gradients in the local information-space ("The Warnings" ) and backtracking up the gradient . If you are in Catastrophe fold (see Postle , catastrophe theory , etc) , backtrack until the fold flattens . This is the optimum exit point . This can always be found unless a Naked Singularity is lurking about .

An application :

Reversing out of a dimly lit underground parking bay at a shopping mall .

The risk of severe neck injuries from even low-speed collisions is distressingly high (in the order of 20% if you have no reverse lights) .

Results of a strapped-in driver suffering a tail-swipe at right-angles :

His body is constrained by the straps and violently torqued , while his head is kept in position by inertia . The neck is violently twisted . The result is damage to the neck muscles , sinews , bloodvessels , vertebra and spinal nerves . Damage can range from whiplash to paralysis , stroke and death . Even from a mild impact .

Drivers looking for parking cruise by at about 20 mph , while their attention is distracted and the lighting is dim . They do not watch for cars moving , but lights moving . The driver reversing out has limited vision due to neighbouring cars and pillars .

These are our warning slopes in the information area .

Optimal Exit Algorithm :1.Do not strap in until outside parking bay . (to stop body-neck twist)2.Switch on lights and a turning signal (to get approaching driver's attention)3.Do not leave anybody outside the car . (Unprotected if metal starts flying around)4.Reverse out carefully in fits and starts (not smoothly) . The approaching driver is not continuously monitoring your area . He must have time to register the change and react .5.Once out , come to a dead stop , strap in and proceed .6. Better if parked with the nose out , but how many people can reverse-park in a narrow parking bay ?7.That’s it .

Your chances of running into a naked singularity in an underground parking space is really small . (Try Las Vegas ?)

Of course , the safest strategy is not to drive at all . This is why this technique is called Optimal , not Best . The most bang for your bucks .

General :The same principles can be applied to get the optimal way out of any situation .

But watch out for naked singularities .These can also be described as strange attractors of strange attractors .